Aliquot sequences that start on the integer powers n^i - Page 7

kar_bon · 2018-11-20, 16:13

11^30 done to 120 digits

garambois · 2018-11-20, 18:04

Quote:

Originally Posted by science_man_88

what other use of powers() in PARI/GP are there ?

Sorry, but I don't exactly understand your question ?

garambois · 2018-11-20, 18:14

Quote:

Originally Posted by gd_barnes

Sweety is not a serious searcher. He just reserves stuff, searches for a little while to a very low search-depth, and then waits for others to extend his searches. You can release all of his reservations for n=12, 13, and 439.

OK, I'll do that in the next week !

And thank you !
I think you're right : 7^96 is now the longest n^i sequence !
Beautiful !

richs and kar_bon thank you too.
I'll update the web page in the next week !

science_man_88 · 2018-11-20, 19:33

Quote:

Originally Posted by garambois

Sorry, but I don't exactly understand your question ?

yeah I was semi joking just thinking of PARI /GP that could be useful.

gd_barnes · 2018-11-21, 08:38

13^30 term 728 merges with sequence 3876 term 11 with a value of 39664.

Sequence 3876 is being worked on by the main project. The reservation for 13^30 can be removed.

garambois · 2018-11-21, 08:41

Quote:

Originally Posted by science_man_88

yeah I was semi joking just thinking of PARI /GP that could be useful.

OK, I see.
The problem is that I have a very poor command of English.
So I often use machine translation.
You must have noticed it !
So I don't always understand some of the subtleties of some messages !

gd_barnes, thank you !

LaurV · 2018-11-21, 09:56

Hey Jean-Luc, Maybe you can add base 28 too... I added few factorization to the DB for 28^n.
I saw you added higher bases, like 439 (?) and I don't know what reason you had, but my opinion is that 28 makes more sense than 439 or 10^x (6^n, 28^n or even 496^n can be seen as powers of perfect numbers, or "powers of drivers", in fact that was what "tickled" my interest for base 6 in the past).

garambois · 2018-11-21, 20:52

OK, the web page is updated.
Thanks to gd_barnes, richs, kar_bon and LaurV for your calculations and proposals !

Quote:

Originally Posted by LaurV

Hey Jean-Luc, Maybe you can add base 28 too... I added few factorization to the DB for 28^n.
I saw you added higher bases, like 439 (?) and I don't know what reason you had, but my opinion is that 28 makes more sense than 439 or 10^x (6^n, 28^n or even 496^n can be seen as powers of perfect numbers, or "powers of drivers", in fact that was what "tickled" my interest for base 6 in the past).

LaurV, I added base 28.
I think that's a good idea !
Besides, it's quite odd that there are only green and blue cells for the moment, but it must be a coincidence !

Some explanations

This web page (aliquot sequences that start on n^i) exists because we have an annoying question on this other web page : http://www.aliquotes.com/existence_s...ini_primes.htm (but sorry in french !).
To try to summarize the question in English :
Can there be an indefinitely growing aliquot sequence in which all terms would be composed of a finite number of prime numbers, but could have any powers ?
We think the answer to that question is "no", but we don't know how to tackle this problem ! However, we would like to get rid of this issue, because we have programs that may be running unnecessarily and are trying to find such aliquot sequences.
The basic idea is therefore to calculate the aliquot sequences that start on integer powers of prime numbers in a first step.
We try very small primes (2, 3, 5...), larger one (439) and a very large one (10^10+19).
We are trying to see if we could "notice" something in the behaviour of these aliquot sequences.
We also do some calculations with slightly composed numbers:
6, 10, 12, 28...
But later, if many people help us with the calculations, we would also like to add the bases with as many prime numbers as possible:
2*3, 2*3*5, 2*3*5*7, 2*3*5*7*11, 2*3*5*7*11*13, .............., and more generally p# with p=53 at least !
Thus, we will observe if the aliquot sequences behave very differently and especially which prime numbers appear in the decomposition of the successive terms of these aliquot sequences.

I hope my explanations are clear !

LaurV · 2018-11-22, 02:18

How often are they updated from the DB?

(for the new addition of 28, the table needs to "pick up" another ~22 green cells, as almost all even powers in the table terminate, some were already terminated by the DB elves, some just needed a little push).

One observation: is it possible to transform javascript links in hard links? One reason, beside of the fact that few people here are scared of javascript (Hello Retina!

), is that the js links are hiding the real link until it is clicked, and when clicked, it opens in another window. If I want to open 5 of them in the same time for comparisons or whatever stupid reason I may have, then I end up with 6 different browsers (including the initial one) floating around my monitors. There is also no way to right click it and tell what to do with the link (like copy it or open it in another place/tab/etc). This looks like a hacker site that deliberately hides the links, and functionally, it is a bit bothering when we want to open more (or all) sequences at once and have them in different tabs in the same browser (actually, impossible to do without heavily altering firefox behavior, because the js link is bypassing the ff's "Open links in tabs instead of new windows" settings).

The "best" workaround I found up to now is to just click the link, then combine the two browsers in one by dragging the tab from the new one to the old one where I have the other tabs. This is easy, but it has the inconvenient that it switches the view to the new tab (well, guess what! I want too much, haha).

About the colors, yes, the "missing" one is orange, but functionally, there is no difference on your site between "orange" and "no color". They all are open sequences, or unknown, or however you want to call them. But I assume your affirmation was a joke related to the fact that you expect(ed) few of us (me) to reserve few of those sequences and work them higher than 120 digits. But don't worry, that time will come...

science_man_88 · 2018-11-22, 02:54

Quote:

Originally Posted by LaurV

One observation: is it possible to transform javascript links in hard links? One reason, beside of the fact that few people here are scared of javascript (Hello Retina!

), is that the js links are hiding the real link until it is clicked, and when clicked, it opens in another window. If I want to open 5 of them in the same time for comparisons or whatever stupid reason I may have, then I end up with 6 different browsers (including the initial one) floating around my monitors. There is also no way to right click it and tell what to do with the link (like copy it or open it in another place/tab/etc). This looks like a hacker site that deliberately hides the links, and functionally, it is a bit bothering when we want to open more (or all) sequences at once and have them in different tabs in the same browser (actually, impossible to do without heavily altering firefox behavior, because the js link is bypassing the ff's "Open links in tabs instead of new windows" settings).

No dev tools? copy the link from there ?

LaurV · 2018-11-22, 03:54

Quote:

Originally Posted by science_man_88

No dev tools? copy the link from there ?

Grrrr...

2018-11-21, 09:56	#73
LaurV Romulan Interpreter "name field" Jun 2011 Thailand 9,973 Posts	Hey Jean-Luc, Maybe you can add base 28 too... I added few factorization to the DB for 28^n. I saw you added higher bases, like 439 (?) and I don't know what reason you had, but my opinion is that 28 makes more sense than 439 or 10^x (6^n, 28^n or even 496^n can be seen as powers of perfect numbers, or "powers of drivers", in fact that was what "tickled" my interest for base 6 in the past). Last fiddled with by LaurV on 2018-11-21 at 09:58

2018-11-22, 02:18	#75
LaurV Romulan Interpreter "name field" Jun 2011 Thailand 9,973 Posts	How often are they updated from the DB? (for the new addition of 28, the table needs to "pick up" another ~22 green cells, as almost all even powers in the table terminate, some were already terminated by the DB elves, some just needed a little push). One observation: is it possible to transform javascript links in hard links? One reason, beside of the fact that few people here are scared of javascript (Hello Retina! ), is that the js links are hiding the real link until it is clicked, and when clicked, it opens in another window. If I want to open 5 of them in the same time for comparisons or whatever stupid reason I may have, then I end up with 6 different browsers (including the initial one) floating around my monitors. There is also no way to right click it and tell what to do with the link (like copy it or open it in another place/tab/etc). This looks like a hacker site that deliberately hides the links, and functionally, it is a bit bothering when we want to open more (or all) sequences at once and have them in different tabs in the same browser (actually, impossible to do without heavily altering firefox behavior, because the js link is bypassing the ff's "Open links in tabs instead of new windows" settings). The "best" workaround I found up to now is to just click the link, then combine the two browsers in one by dragging the tab from the new one to the old one where I have the other tabs. This is easy, but it has the inconvenient that it switches the view to the new tab (well, guess what! I want too much, haha). About the colors, yes, the "missing" one is orange, but functionally, there is no difference on your site between "orange" and "no color". They all are open sequences, or unknown, or however you want to call them. But I assume your affirmation was a joke related to the fact that you expect(ed) few of us (me) to reserve few of those sequences and work them higher than 120 digits. But don't worry, that time will come... Last fiddled with by LaurV on 2018-11-22 at 02:29 Reason: spacing

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2018-11-20, 16:13	#67
kar_bon Mar 2006 Germany 3²×7×47 Posts	11^30 done to 120 digits

2018-11-21, 08:38	#71
gd_barnes May 2007 Kansas; USA 10101010011010₂ Posts	13^30 term 728 merges with sequence 3876 term 11 with a value of 39664. Sequence 3876 is being worked on by the main project. The reservation for 13^30 can be removed.